Mathematical study of feedback control roles and relevance in stress erythropoiesis

This work is devoted to mathematical modelling of erythropoiesis. We propose a new multi-scale model, in which we bring together erythroid progenitor dynamics and intracellular regulatory network that determines erythroid cell fate. All erythroid progenitors are divided into several sub-populations according to their maturity. Two intracellular proteins, Erk and Fas, are supposed to be determinant for regulation of self-renewal, differentiation and apoptosis. We consider two growth factors, erythropoietin and glucocorticoids, and describe their dynamics. Several feedback controls are introduced in the model. We carry out computer simulations of anaemia and compare the obtained results with available experimental data on induced anaemia in mice. The main objective of this work is to evaluate the roles of the feedback controls in order to provide more insights into the regulation of erythropoiesis. Feedback by Epo on apoptosis is shown to be determinant in the early stages of the response to anaemia, whereas regulation through intracellular regulatory network, based on Erk and Fas, appears to operate on a long-term scale.     

A concept of hemopoietic regulation and its biomathematical realization

Although the amount of experimental data on the behavior of the hemopoietic system after various perturbations is considerable, a conclusive understanding of hemopoietic regulation is still absent. In the last years, we have examined murine erythropoiesis, thrombopoiesis, granulopoiesis, and stem cell hemopoiesis by means of mathematical modeling in order to identify some of the underlying principles. Our results can be summarized in four hypotheses. 1) The regulation of hemopoiesis is governed by three interrelated control loops: autoregulation of stem cells, feedback from progenitors and precursors to the stem cells, and feedback from mature cells to progenitor and precursor cells. 2) The feedback from mature cells to the progenitor and precursor cells predominantly varies the number of cell divisions taking place during hemopoietic maturation. 3) Two distinct properties of the stem cells are regulated: their cyclic activity and their self-renewal. Both are under the control of stem cell autoregulation and the feedback from progenitors and precursors. 4) A large variance in the maturation time from the stem cells to the mature cells stabilizes the hemopoietic control. The mathematical formulation of these assumptions allows us to understand a broad range of experimental observations including recovery from stem cell damage, hypoproliferative and hyperproliferative situations, and interactions between different cell lines.     

A multi-scale model of erythropoiesis

In this paper, a multi-scale mathematical model of erythropoiesis is proposed in which erythroid progenitors are supposed to be able to self-renew. Three cellular processes control erythropoiesis: self-renewal, differentiation and apoptosis. We describe these processes and regulatory networks that govern them. Two proteins (ERK and Fas) are considered as the basic proteins participating in this regulation. All erythroid progenitors are divided into several sub-populations depending on their maturity level. Feedback regulations by erythropoietin, glucocorticoids and Fas ligand (FasL) are introduced in the model. The model consists of a system of ordinary differential equations describing intracellular protein concentration evolution and cell population dynamics. We study steady states and their stability. We carry out computer simulations of an anaemia situation and analyse the results.     

A Biomathematical Model of Human Erythropoiesis under Erythropoietin and Chemotherapy Administration

Anaemia is a common haematologic side effect of dose-dense multi-cycle cytotoxic polychemotherapy requiring erythrocyte transfusions or erythropoietin (EPO) administration. To simulate the effectiveness of different EPO application schedules, we performed both modelling of erythropoiesis under chemotherapy and pharmacokinetic and dynamic modelling of EPO applications in the framework of a single comprehensive biomathematical model. For this purpose, a cell kinetic model of bone marrow erythropoiesis was developed that is based on a set of differential compartment equations describing proliferation and maturation of erythropoietic cell stages. The system is regulated by several feedback loops comprising those mediated by EPO. We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications. Chemotherapy is modelled by a transient depletion of bone marrow cell stages. Unknown model parameters were determined by fitting the predictions of the model to data sets of circulating erythrocytes, haemoglobin, haematocrit, percentage of reticulocytes or EPO serum concentrations derived from the literature or cooperating clinical study groups. Parameter fittings resulted in a good agreement of model and data. Depending on site of injection and derivative (Alfa, Beta, Delta, Darbepoetin), nine groups of EPO applications were distinguished differing in either absorption kinetics or pharmacokinetics. Finally, eight different chemotherapy protocols were modelled. The model was validated on the basis of scenarios not used for parameter fitting. Simulations were performed to analyze the impact of EPO applications on the risk of anaemia during chemotherapy. We conclude that we established a model of erythropoiesis under chemotherapy that explains a large set of time series data under EPO and chemotherapy applications. It allows predictions regarding yet untested EPO schedules. Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.     

BMP4/Smad5 dependent stress erythropoiesis is required for the expansion of erythroid progenitors during fetal development

The rapid growth of the embryo places severe demands on the ability of the cardiovascular system to deliver oxygen to cells. To meet this need, erythroid progenitors rapidly expand in the fetal liver microenvironment such that by E14.5, erythropoiesis predominates in the fetal liver. In this report we show that the BMP4/Smad5 dependent stress erythropoiesis pathway plays a key role in the expansion of erythroid progenitors in the fetal liver. These data show that the fetal liver contains two populations of erythroid progenitors. One population resembles the steady state erythroid progenitors found in the adult bone marrow. While the second population exhibits the properties of stress erythroid progenitors found in adult spleen. Here we demonstrate that defects in BMP4/Smad5 signaling preferentially affect the expansion of the stress erythroid progenitors in the fetal liver leading to fetal anemia. These data suggest that steady state erythropoiesis is unable to generate sufficient erythrocytes to maintain the rapid growth of the embryo leading to the induction of the BMP4 dependent stress erythropoiesis pathway. These observations underscore the similarities between fetal erythropoiesis and stress erythropoiesis.     

Progenitor cell self-renewal and cyclic neutropenia

Objectives: Cyclic neutropenia (CN) is a rare genetic disorder where patients experience regular cycling of numbers of neutrophils and various other haematopoietic lineages. The nadir in neutrophil count is the main source of problems due to risk of life-threatening infections. Patients with CN benefit from granulocyte colony stimulating factor therapy, although cycling persists. Mutations in neutrophil elastase gene ( ELA2 ) have been found in more than half of patients with CN. However, neither connection between phenotypic expression of ELA2 and CN nor the mechanism of cycling is known.
Materials and methods:  Recently, a multicompartment model of haematopoiesis that couples stem cell replication with marrow output has been proposed. In the following, we couple this model of haematopoiesis with a linear feedback mechanism via G-CSF.
Results:  We propose that the phenotypic effect of ELA2 mutations leads to reduction in self-renewal of granulocytic progenitors. The body responds by overall relative increase of G-CSF and increasing progenitor cell self-renewal, leading to cell count cycling.
Conclusion:  The model is compatible with available experimental data and makes testable predictions.     

Cep120 and TACCs control interkinetic nuclear migration and the neural progenitor pool

Centrosome- and microtubule-associated proteins have been shown to be important for maintaining the neural progenitor pool during neocortical development by regulating the mitotic spindle. It remains unclear whether these proteins may control neurogenesis by regulating other microtubule-dependent processes such as nuclear migration. Here, we identify Cep120, a centrosomal protein preferentially expressed in neural progenitors during neocortical development. We demonstrate that silencing Cep120 in the developing neocortex impairs both interkinetic nuclear migration (INM), a characteristic pattern of nuclear movement in neural progenitors, and neural progenitor self-renewal. Furthermore, we show that Cep120 interacts with transforming acidic coiled-coil proteins (TACCs) and that silencing TACCs also causes defects in INM and neural progenitor self-renewal. Our data suggest a critical role for Cep120 and TACCs in both INM and neurogenesis. We propose that sustaining INM may be a mechanism by which microtubule-regulating proteins maintain the neural progenitor pool during neocortical development.     

Enforced expression of Hoxa5 in haematopoietic stem cells leads to aberrant erythropoiesis in vivo

Hoxa5 is preferentially expressed in haematopoietic stem cells (HSCs) and multipotent progenitor cells (MPPs), and is more highly expressed in expanding HSCs. To date, little is known regarding the role of Hoxa5 in HSCs and downstream progenitor cells in vivo. In this study, we show that increased expression of Hoxa5 in haematopoietic stem cells leads to aberrant erythropoiesis in vivo. Hoxa5 differentially modifies the cell cycle of HSCs and lineage committed progenitor cells, depending on the cellular context. Hoxa5 drives HSCs, but not MPPs, through the cell cycle and arrests erythroid progenitor cells in G0 phase. Although the HSC pool shrinks after overexpression of Hoxa5, HSCs sustain the abilities of self-renewal and multipotency. In vivo, Hoxa5 has two effects on erythropoiesis: it causes a predominance of mature erythroid lineage cells and the partial apoptosis of erythroid progenitors. RNA-seq indicates that multiple biological processes, including erythrocyte homeostasis, cell metabolism, and apoptosis, are modified by Hoxa5. The results of this study indicate that Hoxa5 is a key regulator of the HSC cell cycle, and the inappropriate expression of Hoxa5 in lineage-committed progenitor cells leads to aberrant erythropoiesis.     

Enforced expression of Hoxa5 in haematopoietic stem cells leads to aberrant erythropoiesis in vivo

Hoxa5 is preferentially expressed in haematopoietic stem cells (HSCs) and multipotent progenitor cells (MPPs), and is more highly expressed in expanding HSCs. To date, little is known regarding the role of Hoxa5 in HSCs and downstream progenitor cells in vivo. In this study, we show that increased expression of Hoxa5 in haematopoietic stem cells leads to aberrant erythropoiesis in vivo. Hoxa5 differentially modifies the cell cycle of HSCs and lineage committed progenitor cells, depending on the cellular context. Hoxa5 drives HSCs, but not MPPs, through the cell cycle and arrests erythroid progenitor cells in G0 phase. Although the HSC pool shrinks after overexpression of Hoxa5, HSCs sustain the abilities of self-renewal and multipotency. In vivo, Hoxa5 has two effects on erythropoiesis: it causes a predominance of mature erythroid lineage cells and the partial apoptosis of erythroid progenitors. RNA-seq indicates that multiple biological processes, including erythrocyte homeostasis, cell metabolism, and apoptosis, are modified by Hoxa5. The results of this study indicate that Hoxa5 is a key regulator of the HSC cell cycle, and the inappropriate expression of Hoxa5 in lineage-committed progenitor cells leads to aberrant erythropoiesis.     

Feedback Signals in Myelodysplastic Syndromes: Increased Self-Renewal of the Malignant Clone Suppresses Normal Hematopoiesis

Myelodysplastic syndromes (MDS) are triggered by an aberrant hematopoietic stem cell (HSC). It is, however, unclear how this clone interferes with physiologic blood formation. In this study, we followed the hypothesis that the MDS clone impinges on feedback signals for self-renewal and differentiation and thereby suppresses normal hematopoiesis. Based on the theory that the MDS clone affects feedback signals for self-renewal and differentiation and hence suppresses normal hematopoiesis, we have developed a mathematical model to simulate different modifications in MDS-initiating cells and systemic feedback signals during disease development. These simulations revealed that the disease initiating cells must have higher self-renewal rates than normal HSCs to outcompete normal hematopoiesis. We assumed that self-renewal is the default pathway of stem and progenitor cells which is down-regulated by an increasing number of primitive cells in the bone marrow niche – including the premature MDS cells. Furthermore, the proliferative signal is up-regulated by cytopenia. Overall, our model is compatible with clinically observed MDS development, even though a single mutation scenario is unlikely for real disease progression which is usually associated with complex clonal hierarchy. For experimental validation of systemic feedback signals, we analyzed the impact of MDS patient derived serum on hematopoietic progenitor cells in vitro: in fact, MDS serum slightly increased proliferation, whereas maintenance of primitive phenotype was reduced. However, MDS serum did not significantly affect colony forming unit (CFU) frequencies indicating that regulation of self-renewal may involve local signals from the niche. Taken together, we suggest that initial mutations in MDS particularly favor aberrant high self-renewal rates. Accumulation of primitive MDS cells in the bone marrow then interferes with feedback signals for normal hematopoiesis – which then results in cytopenia.     

Alpha4beta1 integrin and erythropoietin mediate temporally distinct steps in erythropoiesis: integrins in red cell development

Erythropoietin (Epo) is essential for the terminal proliferation and differentiation of erythroid progenitor cells. Fibronectin is an important part of the erythroid niche, but its precise role in erythropoiesis is unknown. By culturing fetal liver erythroid progenitors, we show that fibronectin and Epo regulate erythroid proliferation in temporally distinct steps: an early Epo-dependent phase is followed by a fibronectin-dependent phase. In each phase, Epo and fibronectin promote expansion by preventing apoptosis partly through bcl-xL. We show that alpha(4), alpha(5), and beta(1) are the principal integrins expressed on erythroid progenitors; their down-regulation during erythropoiesis parallels the loss of cell adhesion to fibronectin. Culturing erythroid progenitors on recombinant fibronectin fragments revealed that only substrates that engage alpha(4)beta(1)-integrin support normal proliferation. Collectively, these data suggest a two-phase model for growth factor and extracellular matrix regulation of erythropoiesis, with an early Epo-dependent, integrin-independent phase followed by an Epo-independent, alpha(4)beta(1)-integrin-dependent phase.     

Stochastic branching model for hemopoietic progenitor cell differentiation

We present algebraic expressions describing the predictions of a stochastic branching model for differentiation of hemopoietic progenitor cells. The model assumes that there is a fixed probability, p (0 less than or equal to p less than or equal to 1), that commitment to a differentiative event occurs per progenitor cell division for each daughter cell. The model describes properties of in vitro hemopoietic cell differentiation including the population structure at the time the first progenitor cell becomes committed, the number of committed progenitor cells engendered by a single progenitor cell, and the probability of eventual commitment of all daughter cells derived from a single progenitor or stem cell. Application of the model to experimental data obtained from erythroid cultures suggests that the observed data can be explained by the stochastic branching model alone without making the deterministic assumption that there is a differentiative hierarchy in the lineage of the progenitors of erythropoiesis (BFU-E). The qualitative and quantitative aspects of the proposed stochastic model are discussed in conjunction with other analogous stochastic branching models.     

Analysis of unstable behavior in a mathematical model for erythropoiesis

We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model.     

Induction and maintenance of specific multipotent progenitor stem cells synergistically mediated by Activin A and BMP4 signaling

We recently reported that epiblast stem cells (EpiSCs)-like cells could be derived from preimplantation embryos (named as AFSCs). Here, we established AFSCs from pre-implantation embryos of multiple mouse strains and showed that unlike EpiSCs, the derivation efficiency of AFSCs was affected by the genetic background. We then used AFSCs lines to dissect the roles of Activin A (Act A) and basic fibroblast growth factor and reported that Act A alone was capable of maintaining self-renewal but not developmental potential in vivo. Finally, we established a novel experimental system, in which AFSCs were efficiently converted to multipotent progenitor stem cells using Act A and bone morphogenetic protein 4 (named as ABSCs). Importantly, these ABSCs contributed to neural mesodermal progenitors and lateral plate mesoderm in postimplantation chimeras. Taken together, our study established a robust experimental system for the generation of specific multipotent progenitor stem cells that was self-renewable and capable of contributing to embryonic and extra-embryonic tissues.     

A novel way to induce erythroid progenitor self renewal: cooperation of c-Kit with the erythropoietin receptor

Red blood cells are of vital importance for oxygen transport in vertebrates. Thus, their formation during development and homeostasis requires tight control of both progenitor proliferation and terminal red cell differentiation. Self renewal (i.e. long-term proliferation without differentiation) of committed erythroid progenitors has recently been shown to contribute to this regulation. Avian erythroid progenitors expressing the EGF receptor/c-ErbB (SCF/TGFalpha progenitors) can be induced to long-term proliferation by the c-ErbB ligand transforming growth factor alpha and the steroids estradiol and dexamethasone. These progenitors have not yet been described in mammals and their factor requirements are untypical for adult erythroid progenitors. Here we describe a second, distinct type of erythroid progenitor (EpoR progenitors) which can be established from freshly isolated bone marrow and is induced to self renew by ligands relevant for erythropoiesis, i.e. erythropoietin, stem cell factor, the ligand for c-Kit and the glucocorticoid receptor ligand dexamethasone. Limiting dilution cloning indicates that these EpoR progenitors are derived from normal BFU-E/CFU-E. For a detailed study, mEpoR progenitors were generated by retroviral expression of the murine Epo receptor in bone marrow erythroblasts. These progenitors carry out the normal erythroid differentiation program in recombinant differentiation factors only. We show that mEpoR progenitors are more mature than SCF/TGFalpha progenitors and also do no longer respond to transforming growth factor alpha and estradiol. In contrast they are now highly sensitive to low levels of thyroid hormone, facilitating their terminal maturation into erythrocytes.     

The kinetics of hematopoietic stem cells during and after hypoxia. A model analysis

A previously described mathematical model of the hematopoietic stem cell system has been extended to permit a detailed understanding of the data during and after hypoxia. The model includes stem cells, erythroid and granuloid progenitors and precursors. Concerning the intramedullary feedback mechanisms two basic assumptions are made: 1) The fraction "a" of CFU-S in active cell cycle is regulated. Reduced cell densities of CFU-S, progenitors or precursors lead to an accelerated stem cell cycling. Enlarged cell densities suppress cycling. 2) The self renewal probability "p" of CFU-S is also regulated. The normal steady state is described by p = 0.5, indicating that on statistical average each dividing mother stem cell is replaced by one daughter stem cell, while the second differentiates. Diminished cell densities of CFU-S or enlarged densities of progenitors and precursors induce a more intensive self renewal (p greater than 0.5), such that the stem cell number increases. The self renewal probability declines (p less than 0.5) if too many CFU-S or too few progenitors and precursors are present. The model reproduces bone marrow data for CFU-S, BFU-E, CFU-C, CFU-E, 59 Fe-uptake and nucleated cells in hypoxia and posthypoxia. Although the ratio of differentiation into the erythroid and granuloid cell lines is kept constant in the model, a changing ratio of CFU-E and CFU-C results. The model suggests that stem cells and progenitor cells are regulated by a regulatory interference of erythropoiesis and granulopoiesis.     

BH3-only protein Noxa contributes to apoptotic control of stress-erythropoiesis

Apoptosis plays an essential role in the control of erythropoiesis under normal and pathological conditions. However, the contribution of individual proteins within cell death signalling pathways remains poorly defined. Here, we investigated the role of the pro-apoptotic Bcl-2 family member Noxa in the regulation of erythropoiesis. We found that expression of Noxa is induced during erythroid differentiation of human and murine precursor cells. Using in vitro model systems for erythroid progenitors, we observed rapid induction of Noxa upon cytokine deprivation. Knockdown or deletion of Noxa conferred significant protection against apoptosis upon cytokine withdrawal. In vivo, Noxa deficiency did not affect hematological blood parameters or erythroid progenitor composition of bone marrow and spleen under steady-state conditions. In contrast, in a model of acute haemolytic anemia, Noxa-deficiency enhanced hematocrit recovery. Moreover, in a model of chronic inflammation-induced anemia, Noxa-ablation resulted in a dramatic increase of erythroblast expansion. Our data indicate that induction of Noxa in erythroid progenitors sets a survival threshold that limits expansion beyond the number of cells that can be sustained by the available cytokines, which becomes apparent under conditions of induced anemia.     

TGF-beta cooperates with TGF-alpha to induce the self-renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism.

Simultaneous addition of both TGF-alpha and TGF-beta induces the sustained, long-term outgrowth of chicken erythrocytic progenitor cells, referred to as T2ECs from both chick bone marrow and 2-day-old chicken embryos. By analysis for differentiation antigens and gene expression, these cells were shown to represent very immature haematopoietic progenitors committed to the erythrocytic lineage. T2ECs differentiate into almost pure populations of fully mature erythrocytes within 6 days, when TGF-alpha and TGF-beta are withdrawn and the cells exposed to anaemic chicken serum plus insulin. Outgrowth of these cells from various sources invariably required both TGF-alpha and TGF-beta, as well as glucocorticoids. Proliferating, established T2ECs still require TGF-alpha, but are independent of exogenous TGF-beta. Using a TGF-beta-neutralizing antibody or expressing a dominant-negative TGF-beta receptor II, we demonstrate that T2ECs generate an autocrine loop involving TGF-beta during their establishment, which is required for sustained proliferation. Using specific inhibitors, we also show that signalling via Mek-1 is specifically required for induction and maintenance of cell proliferation driven by cooperation between the TGF-alpha and -beta receptors. These results establish a novel mechanism by which self-renewal of erythrocytic progenitors is induced and establish avian T2ECs as a new, quasi-optimal model system to study erythrocytic progenitors.